Timeline for Approximating dense subspaces of Fréchet spaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2017 at 9:00 | history | edited | Matthew Daws | CC BY-SA 3.0 |
Big correction
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| Mar 8, 2017 at 20:45 | comment | added | Bill Johnson | @MatthewDaws: That is not the definition of the AP. Moreover, if $E$ is a finite dimensional subspace of a locally convex space $X$, then there is a continuous projection from $X$ onto $E$. | |
| Mar 8, 2017 at 18:20 | comment | added | Martins Bruveris | Thank you for the answer. I checked the details for Fréchet spaces. I can generalize your argument to show that if $H_0$ has the bounded approximation property and admits a continuous norm, then one can construct the sequence of operators $P_n$. In that case the family $(P_n)$ is also equicontinuous. This fits nicely with Jochen's comment, that existence of atomic decompositions is equivalent to the bounded approximation property. | |
| Mar 8, 2017 at 14:21 | history | answered | Matthew Daws | CC BY-SA 3.0 |